\begin{abstract}
%\boldmath
Many real-time systems include tasks that need to suspend their execution in order to externalize some of their operations or to wait for data, events or shared resources. Although commonly encountered in real-world systems, study of their timing analysis is still limited due to the problem complexity. %Traditional timing analyses bypass the harness of the problem by incorporating the suspension delays directly in the task execution requirements. However, those suspension-oblivious techniques may provide pessimistic results when the task suspension times increase. 
In this paper, we invalidate a claim made in one of the earlier works~\cite{Karthik:RTAS10}, that led to the common belief that the timing analysis of one self-suspending task interacting with non-self-suspending sporadic tasks is much easier than in the periodic case. This work highlights the complexity of the problem % and makes an effort in channeling the research efforts on timing analysis of self-suspending tasks back on the right path.
and presents a method to compute the exact worst-case response time (WCRT) of a self-suspending task with one suspension region. However, as the complexity of the analysis might rapidly grow with the number of tasks, we also define an optimization formulation to compute an upper-bound on the WCRT for tasks with multiple suspendion regions. 
In the experiments, our optimization framework outperforms all previous analysis techniques and often finds the exact WCRT.
%In the experimental section, we show that the results output by the optimization problem outperforms all previous analysis techniques and almost always find the exact WCRT.

\end{abstract}